David O’Hallaron Carnegie Mellon University Processor Architecture Logic Design Processor Architecture Logic Design

– 2 – Processor Architecture, PKU Overview of Logic Design Fundamental Hardware Requirements Communication How to get values from one place to another Computation Storage Bits are Our Friends Everything expressed in terms of values 0 and 1 Communication Low or high voltage on wire Computation Compute Boolean functions Storage Store bits of information

– 3 – Processor Architecture, PKU Digital Signals Use voltage thresholds to extract discrete values from continuous signal Simplest version: 1-bit signal Either high range (1) or low range (0) With guard range between them Not strongly affected by noise or low quality circuit elements Can make circuits simple, small, and fast Voltage Time 0 1 0

– 4 – Processor Architecture, PKU Computing with Logic Gates Outputs are Boolean functions of inputs Respond continuously to changes in inputs With some, small delay Voltage Time a b a && b Rising Delay Falling Delay

– 5 – Processor Architecture, PKU Combinational Circuits Acyclic Network of Logic Gates Continously responds to changes on primary inputs Primary outputs become (after some delay) Boolean functions of primary inputs Acyclic Network Primary Inputs Primary Outputs

– 6 – Processor Architecture, PKU Bit Equality Generate 1 if a and b are equal Hardware Control Language (HCL) Very simple hardware description language Boolean operations have syntax similar to C logical operations We’ll use it to describe control logic for processors Bit equal a b eq bool eq = (a&&b)||(!a&&!b) HCL Expression

– 7 – Processor Architecture, PKU Word Equality 32-bit word size HCL representation Equality operation Generates Boolean value b 31 Bit equal a 31 eq 31 b 30 Bit equal a 30 eq 30 b1b1 Bit equal a1a1 eq 1 b0b0 Bit equal a0a0 eq 0 Eq = = B A Word-Level Representation bool Eq = (A == B) HCL Representation

– 8 – Processor Architecture, PKU Bit-Level Multiplexor Control signal s Data signals a and b Output a when s=1, b when s=0 Bit MUX b s a out bool out = (s&&a)||(!s&&b) HCL Expression

– 9 – Processor Architecture, PKU Word Multiplexor Select input word A or B depending on control signal s HCL representation Case expression Series of test : value pairs Output value for first successful test Word-Level Representation HCL Representation b 31 s a 31 out 31 b 30 a 30 out 30 b0b0 a0a0 out 0 int Out = [ s : A; 1 : B; ]; s B A Out MUX

– 10 – Processor Architecture, PKU HCL Word-Level Examples Find minimum of three input words HCL case expression Final case guarantees match A Min3 MIN3 B C int Min3 = [ A < B && A < C : A; B < A && B < C : B; 1 : C; ]; D0 D3 Out4 s0 s1 MUX4 D2 D1 Select one of 4 inputs based on two control bits HCL case expression Simplify tests by assuming sequential matching int Out4 = [ !s1&&!s0: D0; !s1 : D1; !s0 : D2; 1 : D3; ]; Minimum of 3 Words 4-Way Multiplexor

– 11 – Processor Architecture, PKU OF ZF CF OF ZF CF OF ZF CF OF ZF CF Arithmetic Logic Unit Combinational logic Continuously responding to inputs Control signal selects function computed Corresponding to 4 arithmetic/logical operations in Y86 Also computes values for condition codes ALUALU Y X X + Y 0 ALUALU Y X X - Y 1 ALUALU Y X X & Y 2 ALUALU Y X X ^ Y 3 A B A B A B A B

– 12 – Processor Architecture, PKU Storing 1 Bit Bistable Element Q+ Q– q !q q = 0 or 1 V in V1V1 V2V2

– 13 – Processor Architecture, PKU Storing 1 Bit (cont.) Bistable Element Q+ Q– q !q q = 0 or 1 V in V1V1 V2V2 V1V1 V2V2 V in = V 2 Stable 0 Stable 1 Metastable

– 14 – Processor Architecture, PKU Physical Analogy Stable 0 Stable 1 Metastable. Stable left. Stable right. Metastable

– 15 – Processor Architecture, PKU Storing and Accessing 1 Bit Q+ Q– R S R-S Latch Resetting Setting Storing 0 0 !q q q Bistable Element Q+ Q– q !q q = 0 or 1

– 16 – Processor Architecture, PKU 1-Bit Latch D Latch Q+ Q– R S D C Data Clock Latching 1 d!d d dd 0 Storing d!d q !q q 0 0

– 17 – Processor Architecture, PKU Transparent 1-Bit Latch When in latching mode, combinational propogation from D to Q+ and Q– Value latched depends on value of D as C falls Latching 1 d!d d dd C D Q+ Time Changing D

– 18 – Processor Architecture, PKU Edge-Triggered Latch Only in latching mode for brief period Rising clock edge Value latched depends on data as clock rises Output remains stable at all other times Q+ Q– R S D C Data Clock T Trigger C D Q+ Time T

– 19 – Processor Architecture, PKU Registers Stores word of data Different from program registers seen in assembly code Collection of edge-triggered latches Loads input on rising edge of clock IO Clock D C Q+ D C D C D C D C D C D C D C i7i7 i6i6 i5i5 i4i4 i3i3 i2i2 i1i1 i0i0 o7o7 o6o6 o5o5 o4o4 o3o3 o2o2 o1o1 o0o0 Clock Structure

– 20 – Processor Architecture, PKU Register Operation Stores data bits For most of time acts as barrier between input and output As clock rises, loads input State = x Rising clock  Output = xInput = y x  State = y Output = y y

– 21 – Processor Architecture, PKU State Machine Example Accumulator circuit Load or accumulate on each cycle Comb. Logic ALUALU 0 Out MUX 0 1 Clock In Load x0x0 x1x1 x2x2 x3x3 x4x4 x5x5 x0x0 x 0 +x 1 x 0 +x 1 +x 2 x3x3 x 3 +x 4 x 3 +x 4 +x 5 Clock Load In Out

– 22 – Processor Architecture, PKU Random-Access Memory Stores multiple words of memory Address input specifies which word to read or write Register file Holds values of program registers %eax, %esp, etc. Register identifier serves as address »ID 15 (0xF) implies no read or write performed Multiple Ports Can read and/or write multiple words in one cycle »Each has separate address and data input/output Register file Register file A B W dstW srcA valA srcB valB valW Read portsWrite port Clock

– 23 – Processor Architecture, PKU Register File Timing Reading Like combinational logic Output data generated based on input address After some delayWriting Like register Update only as clock rises Register file Register file A B srcA valA srcB valB y 2 Register file Register file W dstW valW Clock x 2 Rising clock   Register file Register file W dstW valW Clock y 2 x 2 x 2

– 24 – Processor Architecture, PKU Hardware Control Language Very simple hardware description language Can only express limited aspects of hardware operation Parts we want to explore and modify Data Types bool : Boolean a, b, c, … int : words A, B, C, … Does not specify word size---bytes, 32-bit words, …Statements bool a = bool-expr ; int A = int-expr ;

– 25 – Processor Architecture, PKU HCL Operations Classify by type of value returned Boolean Expressions Logic Operations a && b, a || b, !a Word Comparisons A == B, A != B, A = B, A > B Set Membership A in { B, C, D } »Same as A == B || A == C || A == D Word Expressions Case expressions [ a : A; b : B; c : C ] Evaluate test expressions a, b, c, … in sequence Return word expression A, B, C, … for first successful test

– 26 – Processor Architecture, PKU Summary Computation Performed by combinational logic Computes Boolean functions Continuously reacts to input changesStorage Registers Hold single words Loaded as clock rises Random-access memories Hold multiple words Possible multiple read or write ports Read word when address input changes Write word as clock rises